Stevin, Simon, Mathematicorum hypomnematum... : T. 4: De Statica : cum appendice et additamentis, 1605

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              <pb o="65" file="527.01.065" n="65" rhead="DE INVENTIONE GRAVITATIS CENTRO."/>
            deinceps in cæteris ſimili machinatione, quorum ſegmentorum ratio per ar-
              <lb/>
            tem cognoſci poſsit. </s>
            <s xml:id="echoid-s2039" xml:space="preserve">C*ONCLVSIO*. </s>
            <s xml:id="echoid-s2040" xml:space="preserve">Quamobrem datis planę ſuperficiæ
              <lb/>
            & </s>
            <s xml:id="echoid-s2041" xml:space="preserve">ſegmenti ejuſdem gravitatis centris & </s>
            <s xml:id="echoid-s2042" xml:space="preserve">C.</s>
            <s xml:id="echoid-s2043" xml:space="preserve"/>
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        <div xml:id="echoid-div310" type="section" level="1" n="222">
          <head xml:id="echoid-head235" xml:space="preserve">7 THEOREMA. 10 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s2044" xml:space="preserve">Parabo.</s>
            <s xml:id="echoid-s2045" xml:space="preserve">æ gravitatis centrum eſt in diametro.</s>
            <s xml:id="echoid-s2046" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2047" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s2048" xml:space="preserve">Parabola A B C, axis A D. </s>
            <s xml:id="echoid-s2049" xml:space="preserve">Q*VÆSITVM*. </s>
            <s xml:id="echoid-s2050" xml:space="preserve">Centrum gravita-
              <lb/>
            tis in A D conſiltere demonſtrato. </s>
            <s xml:id="echoid-s2051" xml:space="preserve">P*RAEPARATIO*. </s>
            <s xml:id="echoid-s2052" xml:space="preserve">E F, G H, I K baſi
              <lb/>
            B C parallelæ interſecent diametrum A D in punctis L, M, N, & </s>
            <s xml:id="echoid-s2053" xml:space="preserve">eædem in-
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            tercipiant rectas E O, G P, I Q, K R, H S, F T axi A D parallelas.</s>
            <s xml:id="echoid-s2054" xml:space="preserve"/>
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        <div xml:id="echoid-div311" type="section" level="1" n="223">
          <head xml:id="echoid-head236" xml:space="preserve">DEMONSTRATIO.</head>
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            <s xml:id="echoid-s2055" xml:space="preserve">Cum enim parallelæ E F, B C, claudantur E O, F T, parallelis, E F T O
              <lb/>
            parallelogrammum erit, cujus oppoſita latera E F, O T in L & </s>
            <s xml:id="echoid-s2056" xml:space="preserve">D bifariam
              <lb/>
            dividuntur, quare centrum gravitatis per 1 propoſ. </s>
            <s xml:id="echoid-s2057" xml:space="preserve">in L D conſiſtet. </s>
            <s xml:id="echoid-s2058" xml:space="preserve">Eadem ra-
              <lb/>
            tione centrũ gravitatis quadranguli G H S P erit in L M, itemq́; </s>
            <s xml:id="echoid-s2059" xml:space="preserve">ipſius IKR Q
              <lb/>
            in M N. </s>
            <s xml:id="echoid-s2060" xml:space="preserve">Quamobrem gravitatis centrum rectilinei I K R H S F T O E P G Q
              <lb/>
            è tribus iſtis parallelogrammis cõflati in DN,
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            ſeu D A conſiſtet. </s>
            <s xml:id="echoid-s2061" xml:space="preserve">Sed quò frequentiora hu-
              <lb/>
            juſmodi parallelogramma in parabolam in-
              <lb/>
            ſcribuntur, eò minor erit inſcriptæ figuræ à
              <lb/>
            parabola defectus. </s>
            <s xml:id="echoid-s2062" xml:space="preserve">Quamobrem infinita hac
              <lb/>
            parallelogrammorum inſcriptione eo adſcen-
              <lb/>
            ditur ut ejus à parabola defectus quacunque
              <lb/>
            minima propoſita ſuperficie minor ſit, conſe-
              <lb/>
            quens igitur eſt, ſumpta A D gravitatis dia-
              <lb/>
            metro, æquilibritatem ſitus ſtgmenti A D C
              <lb/>
            ab æquilibritate ſitus ſegmenti A D B, mi-
              <lb/>
            nori intervallo abeſſe quam vel minimæ quæ
              <lb/>
            dari poſſit ſuperficiei planę differentia: </s>
            <s xml:id="echoid-s2063" xml:space="preserve">unde
              <lb/>
            concludo.</s>
            <s xml:id="echoid-s2064" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s2065" xml:space="preserve">Ponderum inaqualium ſitu gravium differentiâ minus pondus exhiberi poteſt:
              <lb/>
            </s>
            <s xml:id="echoid-s2066" xml:space="preserve">Atqui ponderum horum A D C, A B D ſitu gravium differentiâ pondus minus
              <lb/>
            exhiberinullum poteſt.</s>
            <s xml:id="echoid-s2067" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2068" xml:space="preserve">Ponderum igitur A D C, A B D ſitu gravium differentia nulla eſt.</s>
            <s xml:id="echoid-s2069" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s2070" xml:space="preserve">A D igitur crit diameter gravitatis, & </s>
            <s xml:id="echoid-s2071" xml:space="preserve">propterea parabolæ A B C gravitatis
              <lb/>
            centrum in ipſa. </s>
            <s xml:id="echoid-s2072" xml:space="preserve">C*ONCLVSIO*. </s>
            <s xml:id="echoid-s2073" xml:space="preserve">Itaque paraboles gravitatis centrum eſt in
              <lb/>
            diametro. </s>
            <s xml:id="echoid-s2074" xml:space="preserve">Quod demonſtraſſe oportuit.</s>
            <s xml:id="echoid-s2075" xml:space="preserve"/>
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          <head xml:id="echoid-head237" xml:space="preserve">8 THE OREMA. 11 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s2076" xml:space="preserve">Parabolarum diametri à gravitatis centro in homologa
              <lb/>
            fegmenta dirimuntur.</s>
            <s xml:id="echoid-s2077" xml:space="preserve"/>
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            <s xml:id="echoid-s2078" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s2079" xml:space="preserve">Sunto A B C D & </s>
            <s xml:id="echoid-s2080" xml:space="preserve">a b c d, diſſimiles parabolæ, harum diame-
              <lb/>
            @ri A D, & </s>
            <s xml:id="echoid-s2081" xml:space="preserve">a d, denique gravitatis centra E & </s>
            <s xml:id="echoid-s2082" xml:space="preserve">e.</s>
            <s xml:id="echoid-s2083" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2084" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s2085" xml:space="preserve">Segmenta A E, E D, ſegmentis a e, e d proportionalia
              <lb/>
            @ſſe demonſtrator. </s>
            <s xml:id="echoid-s2086" xml:space="preserve">P*RÆPARATIO*. </s>
            <s xml:id="echoid-s2087" xml:space="preserve">Rectas A B, A C, à vertice </s>
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